Question

the quotient of a number increased by 13 and -7 is -4.

Explanation:

Step1: Define the variable

Let the number be \( x \). The number increased by 13 is \( x + 13 \).

Step2: Set up the equation

The quotient of \( x + 13 \) and -7 is -4, so we can write the equation as \( \frac{x + 13}{-7} = -4 \).

Step3: Solve for \( x \)

Multiply both sides of the equation by -7: \( x + 13 = (-4)\times(-7) \).
Calculate the right side: \( (-4)\times(-7)=28 \), so \( x + 13 = 28 \).
Subtract 13 from both sides: \( x = 28 - 13 \).
Calculate the result: \( x = 15 \).

Answer:

The number is 15.